8) The depth of water in a harbour varies as a function of time. The maximum depth is 9 feet and the

minimum depth is 1 foot. The depth can be modelled with a sinusoidal function that has a period

of 12 hours. If the depth is 5 feet at 12 midnight, and is increasing,

a. Create an algebraic model to predict the depth of the water as a function of time. Justify

your reasoning. {4}

b. The water must be at least 7 feet for Annie's fishing boat to safely navigate the harbour. She

wants to enter the harbour during the afternoon.

i. Sketch a graph of this function. {2}

ii. What is the earliest time she can enter the harbour? {2}

iii. How long can she safely stay in the harbour? {2}